$J$ $K$ $L$ If: $ KL = 6x + 9$, $ JL = 23$, and $ JK = 5x + 3$, Find $KL$.
Solution: From the diagram, we can see that the total length of ${JL}$ is the sum of ${JK}$ and ${KL}$ $ {JK} + {KL} = {JL}$ Substitute in the expressions that were given for each length: $ {5x + 3} + {6x + 9} = {23}$ Combine like terms: $ 11x + 12 = {23}$ Subtract $12$ from both sides: $ 11x = 11$ Divide both sides by $11$ to find $x$ $ x = 1$ Substitute $1$ for $x$ in the expression that was given for $KL$ $ KL = 6({1}) + 9$ Simplify: $ {KL = 6 + 9}$ Simplify to find ${KL}$ : $ {KL = 15}$